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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
The figure above represents a square garden that is divided into 9 rec
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30 Mar 2022, 04:57
30 Mar 2022, 04:57
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The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The figure above represents a square garden that is divided into 9 rec
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30 Mar 2022, 05:35
30 Mar 2022, 05:35
1
GeminiHeat wrote:
The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
The three given lengths on the right sides of the diagram add to 9
Since we're told the garden is a SQUARE, we know that the 3 lengths on the bottom of the diagram must add to 9.
In other words: x + (missing middle length) + 3 = 9
Solve to get: middle length must be 6-x.
At this point, we can find the areas of all 9 rectangles by applying the formula area of rectangle = (base)(height)
The sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes.
We can write: 3x + 3x + 3(6-x) + 9 + 9 = 3x + 3(6-x) + 3(6-x) + 9
Expand: 3x + 3x + 18 - 3x + 9 + 9 = 3x + 18 - 3x + 18 - 3x + 9
Simplify: 3x + 36 = -3x + 45
Add 3x to both sides: 6x + 36 = 45
Subtract 36 from both sides: 6x = 9
Solve: x = 9/6 = 3/2 = 1.5
Answer: C
Cheers,
Brent
gmatclubot
Re: The figure above represents a square garden that is divided into 9 rec [#permalink]
30 Mar 2022, 05:35
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